With health care consuming most of Congress’s bandwidth, Republicans may need to multi-task to achieve other legislative successes this session. Perhaps they could start with reforms to U.S. labor law.

The 1935 National Labor Relations Act hasn’t undergone substantive revisions in 70 years, while the U.S. Constitution has been amended six times. Congress has traditionally deferred to the National Labor Relations Board (NLRB) to interpret labor law, but Barack Obama’s appointees demonstrated the need to safeguard worker rights in statute as they rigged the rules to favor unions.

House Republicans have now introduced an Employee Rights Act partly modeled on state reforms. In the last Congress 137 House Members and 33 Senators co-sponsored similar legislation, which never moved because Mr. Obama had the veto pen. Now they have an ally in the White House.

The House bill would require unions to obtain permission from workers to spend their dues on purposes other than collective bargaining. Current labor law lets unions deduct money from worker paychecks to fund political activities. Workers then must go through the tortuous process of requesting a refund for the share not spent on collective bargaining, which unions may broadly define to include member engagement that boosts voter turnout. No other political outfit enjoys this fundraising fillip.

Democrats oppose an opt-in requirement because they know many workers won’t voluntarily endorse a portion of their paychecks to fund political spending with which they disagree. Exit polls last year showed that 43% of union households voted for Republicans while Democrats received 86% of labor financial support. An opt-in rule could improve political accountability within unions.

Another problem is that only 7% of currently unionized employees voted for their union, according to Bureau of Labor Statistics and NLRB data. Many workforces have turned over completely since their unions were certified. Yet decertifying a union is an arduous process made more difficult by the Obama NLRB.

The House bill would mandate a recertification election upon the expiration of a collective-bargaining agreement if a workforce has turned over by more than 50%. In 2011 Wisconsin passed legislation requiring annual recertification elections for public unions. Membership has since dropped by half as many workers have decided that the costs of belonging exceed the benefits.

Unions sometimes coerce workers into signing cards and then bully employers—for instance, by threatening a public assault on their brand—into recognizing the card checks in lieu of holding secret-ballot elections. The bill would protect workers and employers from union intimidation by taking card-check off the menu of options. It would also allow employees to withhold their personal contact information from unions.

Republicans might not be able to get the 60 votes in the Senate to overcome a filibuster, but they could break up the legislation into bite-sized pieces that could be attached to spending bills. Most provisions poll well and can be easily explained to voters. Let’s see who in Congress will vote to protect workers from coercion.